Question 175
The Fibonacci numbers are defined by $F_{1} = F_{2} = 1$ and $F_{n+2} = F_{n+1} + F_{n}$ for $n \geq 1$. The Lucas numbers are defined by $L_{1} = 1$, $L_{2} = 2$, and $L_{n+2} = L_{n+1} + L_{n}$ for $n \geq 1$. Calculate
$$
\frac{\prod_{n=1}^{15} \frac{F_{2n}}{F_{n}}}{\prod_{n=1}^{13} L_{n}}
$$
$$
\frac{\prod_{n=1}^{15} \frac{F_{2n}}{F_{n}}}{\prod_{n=1}^{13} L_{n}}
$$